The legislation, which cleared the chamber by a vote of 96-49, now heads to the Republican-controlled Senate, where it's expected to pass easily.
Gov. Rick Perry, a Republican, who recently announced he won't seek another term but hasn't ruled out a 2016 presidential run, has said he'll sign the bill. He has been among its most vocal proponents.
The measure has come under the national media spotlight while igniting passionate support from the pro-life community and equally passionate resistance from the pro-choice side. A filibuster by Democratic state Sen. Wendy Davis last month attracted widespread attention and blocked — at least temporarily — passage of the bill. Mr. Perry then called a second special session of the state legislature to take up the bill again.
The governor's tactic was successful, and Ms. Davis and others in the pro-choice camp now concede the bill is destined to become law, possibly as soon as next week with the Senate expected to vote Friday or Saturday.
Moving forward, opponents' strategy will center on drawing as much negative attention as possible to the measure, as well as taking the first steps toward an inevitable federal lawsuit challenging it.
"We will ... be at a place once again where women who have the resources and the ability to access this care will continue to be able to receive that, much like we saw back in the 1950s," Ms. Davis said Wednesday during an interview on MSNBC, an hour after the bill passed. "But women without those resources will turn, unfortunately, to dangerous and very unhealthy alternatives."
Pointing to those "unhealthy alternatives" has already begun in earnest in Austin. Protesters have, for example, brought coat hangers to the Capitol, arguing that women will get back-alley procedures by untrained abortionists if clinics are shut down.
Ms. Davis and other pro-choice advocates note that only about a half-dozen clinics in the state — and none west of San Antonio, an area hundreds of miles wide in all directions — meet the standards and the rest will have to close.
But supporters of the measure, chief among them state Rep. Jody Laubenberg, the prime sponsor of the legislation, say it mostly consists of health-related regulations vital to the safety of patients. They point to such cases as Pennsylvania's Kermit Gosnell and Houston's Douglas Karpen as examples of the kind of unsafe and even deadly mills that underregulated abortion clinics can become.
The bill would require that all doctors who perform abortions also have admitting privileges at an adjoining or nearby hospital. It also outlaws abortions after 20 weeks of pregnancy, outlines when abortion pills can be taken and imposes other regulations upon clinics and providers. Ms. Laubenberg disputed the notion that clinics will close, saying there's nothing in the bill forcing them to shut their doors if they meet the regulations.
Supporters also are casting the bill in a larger, moral context.
Former Arkansas Gov. and Republican presidential candidate Mike Huckabee, who addressed throngs of pro-life supporters in Texas on Monday night, tweeted on Wednesday that "no life is insignificant."
"It is not whether we are for or against abortion but rather whether we believe in the value of every life," he said.
Ms. Laubenberg, who, like Ms. Davis, has become a national political figure because of the abortion bill, expressed similar sentiments.
"What we're talking about today truly is about the health and safety of a woman who would undergo an abortion, but also, I want to point out, we are talking about an unborn child," she said.
Ms. Laubenberg's high profile has turned her into public enemy No. 1 for pro-choice groups such as Planned Parenthood, which has launched a statewide bus tour known as "Stand With Texas Women" designed opposition to the bill.
"It seems like every time women looked up from doing their laundry or helping children with their homework, the Texas legislature is right there taking aim at them again," said group President Cecile Richards.